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    To know a geometric truth (e.g., that an isosceles triang... — Carmelics
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    Supports→Geometric knowledge is grounded in the pure intuition of space rather than in empirical observation or logical analysis alone

    To know a geometric truth (e.g., that an isosceles triangle has two equal base angles), the mathematician must produce a particular spatial construction that makes the truth demonstrable

    PerceptionTruth & Knowledge
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    PerceptionTruth & Knowledge

    Key Terms

    Demonstrable(as used in logic)
    Able to be proven or shown to be true through logical reasoning or evidence.
    geometric truth(as used in mathematics and epistemology)
    A fact about shapes and space that is always true and can be proven through logical reasoning, like how the angles in a triangle always add up to 180 degrees.
    isosceles triangle(as used in geometry)

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    Related propositions within the same area of thought.
    A triangle that has two sides of equal length, which automatically means the two angles opposite those equal sides are also equal.
    spatial construction(as used in mathematics and philosophy of knowledge)
    A drawing or physical arrangement of shapes and lines in space that helps you visualize and understand a mathematical idea.

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    Modality & Possibility1 linked

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    Geometric knowledge is grounded in the pure intuition of space rather than in em...Such constructions appeal to spatial intuition, not mere conceptual analysis or ...

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    One pure mathematical truth can explain another mathematical truth.81%Euclidean geometry possesses certainty and necessity80%Sensitive knowledge of corresponding objects can never achieve the sam...79%Every pure mathematical truth is a necessary truth.79%

    Source

    AI-extracted
    SEP: epistemology-geometry
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    In Kant’s Critique of Pure Reason (1781/1787) (see the entry Kant’s views on space and time) the situation is more complicated or sophisticated. Kant introduced the notion of a priori knowledge in contrast to a posteriori, and synthetic knowledge in contrast to analytical knowledge to allow for the existence of knowledge that did not rely on experience (and was thus a priori) but was not tautological in character (and therefore synthetic and not analytic). The contentious class of synthetic a

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